Abstract

We investigate models of supersymmetric grand unification based on the gauge groups SU(5), SO(10) and E_6, as well as in a class of orbifolds inspired by four dimensional Strings. We follow a stepwise analysis starting our journey with a revisit to the Standard Model and commenting on major issues that are motivation for new physics. We then introduce supersymmetry and discuss the Minimal Supersymmetric Standard Model (MSSM), with a detailed analysis of its mass spectrum. We study the evolution of the strong and electroweak forces with the energy scale, and interpret the near match of the gauge couplings at the high scale as a clue for the unification of strong and electroweak interactions.

The second half of our journey starts with the introduction of the SU(5), SO(10) and E_6 symmetries. We provide a review of main aspects such as proton stability, split multiplets and Yukawa unification, and show how the MSSM soft parameters may be constrained by these groups. We demonstrate how the measurement of the first and second generation supersymmetric spectrum may be used to probe the underlying grand unification structure and compare our expressions with numerical calculations. We consider SU(5) and SO(10) models with non-universal gaugino masses and confront them with low energy constraints, including the Higgs boson mass and the Dark Matter relic density. We also discuss fine-tuning and show the effect of not including the mu-parameter into fine tuning determinations. With this relaxation, we find viable scenarios with low fine tuning and study some model choices for gaugino mass ratios. We demonstrate that gaugino masses inspired by some orbifold models may provide low fine-tuning and the preferred relic abundance of Dark Matter while evading all experimental constraints. We also determine high scale Yukawa coupling ratios and confront the results with theoretical predictions. We finally consider orbifold models to constrain the full set of soft parameters, and argue that a String inspired framework presents definite theoretical background to relax fine-tuning constraints. We present benchmarks for all our scenarios that should be explored at the LHC and future colliders.